This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A202842 #9 Mar 05 2020 12:24:01 %S A202842 1,1,1,2,4,7,14,31,66,142,316,708,1593,3625,8314,19165,44433,103557, %T A202842 242376,569514,1343099,3177766,7540845,17943506,42804078,102345017, %U A202842 245233366,588785677,1416247791,3412495415,8235829927,19906780104,48185131721,116790380824,283432579807 %N A202842 Number of secondary structures of size n having no stacks of length 2. %C A202842 For "secondary structure" and "stack" see the Hofacker et al. reference, p. 209. %C A202842 a(n) = A202841(n,0). %H A202842 I. L. Hofacker, P. Schuster and P. F. Stadler, <a href="https://doi.org/10.1016/S0166-218X(98)00073-0">Combinatorics of RNA secondary structures</a>, Discrete Appl. Math., 88, 1998, 207-237. %H A202842 P. R. Stein and M. S. Waterman, <a href="https://doi.org/10.1016/0012-365X(79)90033-5">On some new sequences generalizing the Catalan and Motzkin numbers</a>, Discrete Math., 26 (1979), 261-272. %F A202842 G.f.: G=G(z) satisfies G = 1+zG +fG(G-1)/(1+f), where f = z^2*(1-z^2+z^4)/(1-z^2). %e A202842 a(5)=7; representing unpaired vertices by v and arcs by AA, BB, etc., the 8 (= A004148(5)) secondary structures of size 5 are vvvvv, AvAvv, vvAvA, AvvAv, vAvvA, AvvvA, vAvAv, ABvBA; only the last one has a stack of length 2. %p A202842 f := z^2*(1-z^2+z^4)/(1-z^2): eq := G = 1+z*G+f*G*(G-1)/(1+f): G := RootOf(eq, G): Gser := simplify(series(G, z = 0, 38)): seq(coeff(Gser, z, n), n = 0 .. 34); %Y A202842 Cf. A202838, A202839, A202840, A202841, A202843, A202844 %K A202842 nonn %O A202842 0,4 %A A202842 _Emeric Deutsch_, Dec 25 2011